Traditional end-to-end contextual robust optimization models are trained for specific contextual data, requiring complete retraining whenever new contextual information arrives. This limitation hampers their use in online decision-making problems such as energy scheduling, where multiperiod optimization must be solved every few minutes. In this paper, we propose a novel Data-Driven Contextual Uncertainty Set, which gives rise to a new End-to-End Data-Driven Contextual Robust Optimization model. For right-hand-side uncertainty, we introduce a reformulation scheme that enables the development of a variant of the Column-and-Constraint Generation (CCG) algorithm. This new CCG method explicitly considers the contextual vector within the cut expressions, allowing previously generated cuts to remain valid for new contexts, thereby significantly accelerating convergence in online applications. Numerical experiments on energy and reserve scheduling problems, based on classical test cases and large-scale networks (with more than 10,000 nodes), demonstrate that the proposed method reduces computation times and operational costs while capturing context-dependent risk structures. The proposed framework (model and method), therefore, offers a unified, scalable, and prescriptive approach to robust decision-making under uncertainty, effectively bridging data-driven learning and optimization.

The recent interest in contextual optimization problems, where randomness is associated with side information, has led to two primary strategies for formulation and solution. The first, estimate-then-optimize, separates the estimation of the problem's parameters from the optimization process. The second, decision-focused optimization, integrates the optimization problem's structure directly into the prediction procedure. In this work, we propose a pessimistic bilevel approach for solving general decision-focused formulations of combinatorial optimization problems. Our method solves an $\varepsilon$-approximation of the pessimistic bilevel problem using a specialized cut generation algorithm. We benchmark its performance on the 0-1 knapsack problem against estimate-then-optimize and decision-focused methods, including the popular SPO+ approach. Computational experiments highlight the proposed method's advantages, particularly in reducing out-of-sample regret.

The Federal Funds rate in the United States plays a significant role in both domestic and international financial markets. However, research has predominantly focused on the effects of adjustments to the Federal Funds rate rather than on the decision-making process itself. Recent advancements in large language models(LLMs) offer a potential method for reconstructing the original FOMC meetings, which are responsible for setting the Federal Funds rate. In this paper, we propose a five-stage FOMC meeting simulation framework, MiniFed, which employs LLM agents to simulate real-world FOMC meeting members and optimize the FOMC structure. This framework effectively revitalizes the FOMC meeting process and facilitates projections of the Federal Funds rate. Experimental results demonstrate that our proposed MiniFed framework achieves both high accuracy in Federal Funds rate projections and behavioral alignment with the agents' real-world counterparts. Given that few studies have focused on employing LLM agents to simulate large-scale real-world conferences, our work can serve as a benchmark for future developments.

Network connections, both across and within markets, are central in countless economic contexts. In recent decades, a large literature has developed and applied flexible methods for measuring network connectedness and its evolution, based on variance decompositions from vector autoregressions (VARs), as in Diebold and Yilmaz (2014). Those VARs are, however, typically identified using full orthogonalization (Sims, 1980), or no orthogonalization (Koop, Pesaran, and Potter, 1996; Pesaran and Shin, 1998), which, although useful, are special and extreme cases of a more general framework that we develop in this paper. In particular, we allow network nodes to be connected in "clusters", such as asset classes, industries, regions, etc., where shocks are orthogonal across clusters (Sims style orthogonalized identification) but correlated within clusters (Koop-Pesaran-Potter-Shin style generalized identification), so that the ordering of network nodes is relevant across clusters but irrelevant within clusters. After developing the clustered connectedness framework, we apply it in a detailed empirical exploration of sixteen country equity markets spanning three global regions.

We build an agent-based model to study how the interplay between low- and high-frequency trading affects asset price dynamics. Our main goal is to investigate whether high-frequency trading exacerbates market volatility and generates flash crashes. In the model, low-frequency agents adopt trading rules based on chronological time and can switch between fundamentalist and chartist strategies. On the contrary, high-frequency traders activation is event-driven and depends on price fluctuations. High-frequency traders use directional strategies to exploit market information produced by low-frequency traders. Monte-Carlo simulations reveal that the model replicates the main stylized facts of financial markets. Furthermore, we find that the presence of high-frequency trading increases market volatility and plays a fundamental role in the generation of flash crashes. The emergence of flash crashes is explained by two salient characteristics of high-frequency traders, i.e. their ability to i) generate high bid-ask spreads and ii) synchronize on the sell side of the limit order book. Finally, we find that higher rates of order cancellation by high-frequency traders increase the incidence of flash crashes but reduce their duration.

Parkinson's disease is a neurological condition that occurs in nearly 1% of the world's population. The disease is manifested by a drop in dopamine production, symptoms are cognitive and behavioural and include a wide range of personality changes, depressive disorders, memory problems, and emotional dysregulation, which can occur as the disease progresses. Early diagnosis and accurate staging of the disease are essential to apply the appropriate therapeutic approaches to slow cognitive and motor decline. Currently, there is not a single blood test or biomarker available to diagnose Parkinson's disease. Magnetic resonance imaging has been used for the past three decades to diagnose and distinguish between PD and other neurological conditions. However, in recent years new possibilities have arisen: several AI algorithms have been developed to increase the precision and accuracy of differential diagnosis of PD at an early stage. To our knowledge, no AI tools have been designed to identify the stage of progression. This paper aims to fill this gap. Using the "Parkinson's Progression Markers Initiative" dataset, which reports the patient's MRI and an indication of the disease stage, we developed a model to identify the level of progression. The images and the associated scores were used for training and assessing different deep-learning models. Our analysis distinguished four distinct disease progression levels based on a standard scale (Hoehn and Yah scale). The final architecture consists of the cascading of a 3DCNN network, adopted to reduce and extract the spatial characteristics of the RMI for efficient training of the successive LSTM layers, aiming at modelling the temporal dependencies among the data. Our results show that the proposed 3DCNN + LSTM model achieves state-of-the-art results by classifying the elements with 91.90\% as macro averaged OVR AUC on four classes

We study a class of multi-stage stochastic programs, which incorporate modeling features from Markov decision processes (MDPs). This class includes structured MDPs with continuous state and action spaces. We extend policy graphs to include decision-dependent uncertainty for one-step transition probabilities as well as a limited form of statistical learning. We focus on the expressiveness of our modeling approach, illustrating ideas with a series of examples of increasing complexity. As a solution method, we develop new variants of stochastic dual dynamic programming, including approximations to handle non-convexities.

Accumulated Local Effects (ALE) is a model-agnostic approach for global explanations of the results of black-box machine learning (ML) algorithms. There are at least three challenges with conducting statistical inference based on ALE: ensuring the reliability of ALE analyses, especially in the context of small datasets; intuitively characterizing a variable's overall effect in ML; and making robust inferences from ML data analysis. In response, we introduce innovative tools and techniques for statistical inference using ALE, establishing bootstrapped confidence intervals tailored to dataset size and introducing ALE effect size measures that intuitively indicate effects on both the outcome variable scale and a normalized scale. Furthermore, we demonstrate how to use these tools to draw reliable statistical inferences, reflecting the flexible patterns ALE adeptly highlights, with implementations available in the 'ale' package in R. This work propels the discourse on ALE and its applicability in ML and statistical analysis forward, offering practical solutions to prevailing challenges in the field.

Judicial opinions once considered sound can lose relevance over time. Yet, little has been known, both systematically and at scale, about how judicial reasoning has evolved. Here, we analyze four million US court decisions from 1800 to 2000, quantifying each rulings' disruptiveness, i.e., the extent to which it breaks from established citation pathways. We find that such pathbreaks have declined over time, indicating that courts have become increasingly constrained by precedent. This growing inertia appears to be driven by two structural factors. The first is precedent overload, evidenced by the volume of case law outpacing population growth (scaling exponent of 1.7). The second is the rise of ideological polarization within the judiciary, which introduces institutional uncertainty that prompts greater deference to established precedent. Despite this overall tendency toward path dependence, we find that a relatively small number of high-authority courts continue to shape legal discourse through top-down interventions. Our findings recast legal reasoning as an evolutionary process shaped by structural growth, institutional memory, and hierarchical structure, incorporating broader theories of innovation and organizational adaptation into the study of law.

The present study proposes a new index to quantify the severity of non-stationary power quality (PQ) disturbance events. In particular, the severity of PQ events is estimated from their energy distribution in temporal-frequency space. The index essentially measures the $\ell_p$-norm between the energy distributions of an event and the nominal voltage signal. The efficacy of the new index is demonstrated considering a wide class of major non-stationary PQ events, including sag, swell, interruptions, oscillatory transients, and simultaneous events. The results of this investigation, with simulated, real and experimental data, convincingly demonstrate that the proposed index is generic, monotonic, easy to interpret, and can accurately quantify the severity of non-stationary events.

Classical Cellular Automata (CCAs) are a powerful computational framework widely used to model complex systems driven by local interactions. Their simplicity lies in the use of a finite set of states and a uniform local rule, yet this simplicity leads to rich and diverse dynamical behaviors. CCAs have found applications in numerous scientific fields, including quantum computing, biology, social sciences, and cryptography. However, traditional CCAs assume complete certainty in the state of all cells, which limits their ability to model systems with inherent uncertainty. This paper introduces a novel generalization of CCAs, termed Cellular Automata on Measures (CAMs), which extends the classical framework to incorporate probabilistic uncertainty. In this setting, the state of each cell is described by a probability measure, and the local rule operates on configurations of such measures. This generalization encompasses the traditional Bernoulli measure framework of CCAs and enables the study of more complex systems, including those with spatially varying probabilities. We provide a rigorous mathematical foundation for CAMs, demonstrate their applicability through concrete examples, and explore their potential to model the dynamics of random graphs. Additionally, we establish connections between CAMs and symbolic dynamics, presenting new avenues for research in random graph theory. This study lays the groundwork for future exploration of CAMs, offering a flexible and robust framework for modeling uncertainty in cellular automata and opening new directions for both theoretical analysis and practical applications.

The balanced connected $k$-partition problem (BCP) is a classic problem which consists in partitioning the set of vertices of a vertex-weighted connected graph into a collection of $k$ sets such that each of them induces a connected subgraph of roughly the same weight. There exists a vast literature on BCP that includes hardness results, approximation algorithms, integer programming formulations, and a polyhedral study. We investigate edge-weighted variants of BCP where we are given a connected graph $G$, $k \in \mathbb{Z}_\ge$, and an edge-weight function $w \colon E(G)\to\mathbb{Q}_\ge$, and the goal is to compute a spanning $k$-forest $\mathcal{T}$ of $G$ (i.e., a forest with exactly $k$ trees) that minimizes the weight of the heaviest tree in $\mathcal{T}$ in the min-max version, or maximizes the weight of the lightest tree in $\mathcal{T}$ in the max-min version. We show that both versions of this problem are $\mathsf{NP}$-hard on complete graphs with $k=2$, unweighted split graphs, and unweighted bipartite graphs with $k\geq 2$ fixed. Moreover, we prove that these problems do not admit subexponential-time algorithms, unless the Exponential-Time Hypothesis fails. Finally, we devise compact and non-compact integer linear programming formulations, valid inequalities, and separation algorithms.

Classical Cellular Automata (CCAs) are a powerful computational framework for modeling global spatio-temporal dynamics with local interactions. While CCAs have been applied across numerous scientific fields, identifying the local rule that governs observed dynamics remains a challenging task. Moreover, the underlying assumption of deterministic cell states often limits the applicability of CCAs to systems characterized by inherent uncertainty. This study, therefore, focuses on the identification of Cellular Automata on spaces of probability measures (CAMs), where cell states are represented by probability distributions. This framework enables the modeling of systems with probabilistic uncertainty and spatially varying dynamics. Moreover, we formulate the local rule identification problem as a parameter estimation problem and propose a meta-heuristic search based on Self-adaptive Differential Evolution (SaDE) to estimate local rule parameters accurately from the observed data. The efficacy of the proposed approach is demonstrated through local rule identification in two-dimensional CAMs with varying neighborhood types and radii.

We model a competitive market where AI agents buy answers from upstream generative models and resell them to users who differ in how much they value accuracy and in how much they fear hallucinations. Agents can privately exert effort for costly verification to lower hallucination risks. Since interactions halt in the event of a hallucination, the threat of losing future rents disciplines effort. A unique reputational equilibrium exists under nontrivial discounting. The equilibrium effort, and thus the price, increases with the share of users who have high accuracy concerns, implying that hallucination-sensitive sectors, such as law and medicine, endogenously lead to more serious verification efforts in agentic AI markets.

Alternative data sets are widely used for macroeconomic nowcasting together with machine learning--based tools. The latter are often applied without a complete picture of their theoretical nowcasting properties. Against this background, this paper proposes a theoretically grounded nowcasting methodology that allows researchers to incorporate alternative Google Search Data (GSD) among the predictors and that combines targeted preselection, Ridge regularization, and Generalized Cross Validation. Breaking with most existing literature, which focuses on asymptotic in-sample theoretical properties, we establish the theoretical out-of-sample properties of our methodology and support them by Monte-Carlo simulations. We apply our methodology to GSD to nowcast GDP growth rate of several countries during various economic periods. Our empirical findings support the idea that GSD tend to increase nowcasting accuracy, even after controlling for official variables, but that the gain differs between periods of recessions and of macroeconomic stability.

In this paper, we study a mixed variational problem subject to perturbations, where the noise term is modelled by means of a bilinear form that has to be understood to be "small" in some sense. Indeed, we consider a family of such problems and provide a result that guarantees existence and uniqueness of the solution. Moreover, a stability condition for the solutions yields a Generalized Collage Theorem, which extends previous results by the same authors. We introduce the corresponding Galerkin method and study its convergence. We also analyze the associated inverse problem and we show how to solve it by means of the mentioned Generalized Collage Theorem and the use of adequate Schauder bases. Numerical examples show how the method works in a practical context.

We study how network structure affects the dynamics of collateral in presence of rehypothecation. We build a simple model wherein banks interact via chains of repo contracts and use their proprietary collateral or re-use the collateral obtained by other banks via reverse repos. In this framework, we show that total collateral volume and its velocity are affected by characteristics of the network like the length of rehypothecation chains, the presence or not of chains having a cyclic structure, the direction of collateral flows, the density of the network. In addition, we show that structures where collateral flows are concentrated among few nodes (like in core-periphery networks) allow large increases in collateral volumes already with small network density. Furthermore, we introduce in the model collateral hoarding rates determined according to a Value-at-Risk (VaR) criterion, and we then study the emergence of collateral hoarding cascades in different networks. Our results highlight that network structures with highly concentrated collateral flows are also more exposed to large collateral hoarding cascades following local shocks. These networks are therefore characterized by a trade-off between liquidity and systemic risk.

Large-scale data analysis is growing at an exponential rate as data proliferates in our societies. This abundance of data has the advantage of allowing the decision-maker to implement complex models in scenarios that were prohibitive before. At the same time, such an amount of data requires a distributed thinking approach. In fact, Deep Learning models require plenty of resources, and distributed training is needed. This paper presents a Multicriteria approach for distributed learning. Our approach uses the Weighted Goal Programming approach in its Chebyshev formulation to build an ensemble of decision rules that optimize aprioristically defined performance metrics. Such a formulation is beneficial because it is both model and metric agnostic and provides an interpretable output for the decision-maker. We test our approach by showing a practical application in electricity demand forecasting. Our results suggest that when we allow for dataset split overlapping, the performances of our methodology are consistently above the baseline model trained on the whole dataset.

Limited English Proficiency (LEP) patients face higher risks of adverse health outcomes due to communication barriers, making timely medical interpreting services essential for mitigating those risks. This paper addresses the scheduling of medical interpreting services under uncertainty. The problem is formulated as a two-stage stochastic programming model that accounts for uncertainties in emergency patients' arrival and service time. The model handles the hiring decisions of part-time interpreters and the assignment of full-time and hired part-time interpreters. The objective is to minimize the total cost, which encompasses full-time interpreters' overtime cost, the fixed and variable costs of part-time interpreters, and the penalty cost for not serving LEP patients on time. The model is solved using the Sample Average Approximation (SAA) algorithm. To overcome the computational burden of the SAA algorithm, a Tabu Search (TS) algorithm was used to solve the model. A real-life case study is used to validate and evaluate the proposed solution algorithms. The results demonstrate the effectiveness of the proposed stochastic programming-based solutions in concurrently reducing both the total cost and the waiting time. Further, sensitivity analysis reveals how the increase in some key parameters, such as the arrival rate of emergency patients with LEP, impacts scheduling outcomes.

The optimal allocation of vaccines to population subgroups over time is a challenging health care management problem. In the context of a pandemic, the interaction between vaccination policies adopted by multiple agents and the cooperation (or lack thereof) creates a complex environment that affects the global transmission dynamics of the disease. In this study, we take the perspective of decision-making agents that aim to minimize the size of their susceptible populations and must allocate vaccine under limited supply. We assume that vaccine efficiency rates are unknown to agents and we propose an optimization policy based on Thompson sampling to learn mean vaccine efficiency rates over time. Furthermore, we develop a budget-balanced resource sharing mechanism to promote cooperation among agents. We apply the proposed framework to the COVID-19 pandemic. We use a raster model of the world where agents represent the main countries worldwide and interact in a global mobility network to generate multiple problem instances. Our numerical results show that the proposed vaccine allocation policy achieves a larger reduction in the number of susceptible individuals, infections and deaths globally compared to a population-based policy. In addition, we show that, under a fixed global vaccine allocation budget, most countries can reduce their national number of infections and deaths by sharing their budget with countries with which they have a relatively high mobility exchange. The proposed framework can be used to improve policy-making in health care management by national and global health authorities.